Answer:
C) A coordinate grid with one line that passes through the points (0, 1) and (1, 2) and another line that passes through the points (0, 0) and (1, 4).
Step-by-step explanation:
Given system of linear equations:
[tex]\begin{cases}y = 4x\\y = x + 1\end{cases}[/tex]
To determine the graph of the system of equations, we can find two points on each line by substituting x = 0 and x = 1 into each equation:
[tex]\begin{aligned}\boxed{y=4x}\quad x=0 \implies y&=4(0)\\y&=0\end{aligned}[/tex]
[tex]\begin{aligned}\boxed{y=4x}\quad x=1 \implies y&=4(1)\\y&=4\end{aligned}[/tex]
[tex]\begin{aligned}\boxed{y=x+1}\quad x=0 \implies y&=0+1\\y&=1\end{aligned}[/tex]
[tex]\begin{aligned}\boxed{y=x+1}\quad x=1 \implies y&=1+1\\y&=2\end{aligned}[/tex]
Therefore, one line passes through points (0, 0) and (1, 4), and the other line passes through points (0, 1) and (1, 2).
The solution to a system of linear equations is the point of intersection of the two lines.
To find the solution to the system of linear equations y = 4x and y = x + 1, we can set the expressions for y equal to each other, then solve for x:
[tex]\begin{aligned}4x&=x+1\\\\4x-x&=x+1-x\\\\3x&=1\\\\\dfrac{3x}{3}&=\dfrac{1}{3}\\\\x&=\dfrac{1}{3}\end{aligned}[/tex]
Now that we have the value for x, substitute it back into either of the original equations to find the corresponding y-coordinate. Let's use y = 4x:
[tex]\begin{aligned}y&=4\cdot \dfrac{1}{3}\\\\y&=\dfrac{4}{3}\end{aligned}[/tex]
So, the solution to the system of equations is the point:
[tex]\left(\dfrac{1}{3}, \dfrac{4}{3}\right)[/tex]
